The chord progression is the same….Which means jackshit unless she's writing the instrumentals, which I doubt. I'm pretty sure Katy only writes melodies and the chorus/verses of Roar sound nothing like Brave

They are similar, but the main difference between Katy and Sarah's songs is that Sarah is actually a really talented singer. I love some Katy Perry, but have you heard her live? Oy vey. Sarah wins that battle hands down, so I don't think she feels like she is competing against much.